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You have to take it to a Sony repair center and/or back to the store.
I have same kind of issues but only on certain surfaces. It somehow depends on surface my Z1 is lying on. If i put my phone on my bed touch screen doesn't respond as it should but when I hold it flat or put it on wooden table it works as it should. Also if it's lying on my bed and I touch it's frame with my other hand the touch screen starts to work as it should. Verry strange.